According to Catagolue, it is the fifty-seventh most common object in even 8-fold symmetry (D8_4), occurring in 1 in 4600 soups.
Extensions
Cross is the smallest in an infinite family of period 3 oscillators, the next of which is cross 2. The fact that this infinite family of oscillators exists shows that there are an infinite number of oscillators that are polyominoes in at least one of their phases.
An alternate form of extension can be derived from the fact that one of its phases involves four detached segments. Two other oscillators, the pulsar and bracket pulsar, visually resemble this phase, and the cross can be extended in much the same way as these other oscillators can.
